Isometric Reflectionless Eigenfunction Transforms for Higher-order AOs
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In a previous paper (Regular and Chaotic Dynamics 7 (2002), 351391, Ref. ), we obtained various results concerning reflectionless Hilbert space transforms arising from a general Cauchy system. Here we extend these results, proving in particular an isometry property conjectured in Ref. . Crucial input for the proof comes from previous work on a special class of relativistic Calogero-Moser systems. Specifically, we exploit results on action-angle maps for the pertinent systems and their relation to the 2D Toda soliton tau-functions. The reflectionless transforms may be viewed as eigenfunction transforms for an algebra of higher-order analytic difference operators.
- © 2006, the Authors. Published by Atlantis Press.
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Cite this article
TY - JOUR AU - S.N.M. Ruijsenaars PY - 2005 DA - 2005/01/01 TI - Isometric Reflectionless Eigenfunction Transforms for Higher-order AOs JO - Journal of Nonlinear Mathematical Physics SP - 565 EP - 598 VL - 12 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2005.12.s1.45 DO - 10.2991/jnmp.2005.12.s1.45 ID - Ruijsenaars2005 ER -